Meeting 1 (13.10.2025 by Keremcan Doğan): Introduction and motivation, Algebra and geometry correspondence, A little history of geometry and physics, Klein and Erlangen program, Noether theorem, Galilean and Poincare groups, Group representations, Wigner classification, Dirac equation
Meeting 2 (27.10.2025 by Bilal Bulduk): Quadratic vector spaces, Clifford algebras, Gamma matrices, Low dimensional examples, Z_2 grading, Exterior algebra, Clifford algebra chessboard, Bott periodicity, Orthogonal group and its Lie algebra (Jose Figueroa-O’Farrill lecture notes, Spin geometry Section 1.1, 1.3, 1.4, 3.1)
Meeting 3 (17.11.2025 by Oğuzhan Selçuk): Adjoint and twisted adjoint actions, Pin and spin groups, Exact sequences for Pin(V)-O(V) and Spin(V)-SO(V) and double covering, Group representations, Pin and spin representations (Jose Figueroa-O’Farrill lecture notes, Spin geometry Section 3.2, 3.3)
Meeting 4 (24.11.2025 by Oğuzhan Selçuk): Complexification of Clifford algebras, An example of pin and spin representations for 2-dimensional complexified Clifford algebra via Pauli matrices, Topological and smooth manifolds, Coordinate charts and transition maps, Fiber bundles, Transition maps and local trivializations, Vector bundle, Tangent bundle (Jose Figueroa-O’Farrill lecture notes, Spin geometry Section 4.1, 4.2.1, 4.2.2)
Meeting 5 (08.12.2025 by Oğuzhan Selçuk): Principal G-bundles, Vector bundles and principal bundles correspondece, Frame bundles, Associated bundles, Orthonormal frame bundle, Special orthonormal frame bundle, Spin bundle (spin structure), Stiefel-Whitney classes for obstruction (Jose Figueroa-O’Farrill lecture notes, Spin geometry Section 4.2.3, 4.3.1, 4.3.3)
Meeting 6 (22.12.2025 by Deniz Ergül): Connections, Metric-affine geometry, Lie bracket, Torsion, Curvature, Non-metricity, Levi-Civita connections, Koszul formula, Algebraic and differential Bianchi identities, Algebraic curvature tensor, Ricci tensor and Ricci scalar, Einstein manifolds, Kulkarni-Nomizu product, Decomposition of Riemann curvature tensor (Jose Figueroa-O’Farrill lecture notes, Spin geometry Section 6.1)
Meeting 7 (29.12.2025 by Deniz Ergül): Push-forward and pull-back, Functoriality of tangent and cotangent constructions, Vertical and horizontal subspaces on principal bundles, Isomorphism between the vertical subspace and the Lie algebra via the orbit map, Ehresmann connections
Meeting 8 (05.01.2026 by Deniz Ergül): Connection 1-form, Horizontal projection, Curvature 2-form, Exterior derivative, Exterior derivative of valued forms, Koszul connection, Basic forms